Numerical realization of the generalized Carrier-Greenspan transform for the shallow water wave equations

• Main Author: Harris, Matthew W.
• Language: EN
• Published: University of Alaska Fairbanks 2015
• Subjects: Applied mathematics|Geophysics|Mathematics
• Online Access: http://pqdtopen.proquest.com/#viewpdf?dispub=1598961

<p> Run-up of long waves in sloping U-shaped bays is studied analytically in the framework of the 1-D nonlinear shallow-water theory. By assuming that the wave flow is uniform along the cross-section, the 2-D nonlinear shallow-water equations are reduced to a linear semi-axis variable-coefficient 1-D wave equation via the generalized Carrier-Greenspan transformation (Rybkin et al., 2014). A spectral solution is developed by solving the linear semiaxis variable-coefficient 1-D equation via separation of variables and then applying the inverse Carrier-Greenspan transform. To compute the run-up of a given long wave a numerical method is developed to find the eigenfunction decomposition required for the spectral solution in the linearized system. The run-up of a long wave in a bathymetry characteristic of a narrow canyon is then examined.</p>